An extension of the Hermite-Hadamard inequality for a power of a convex function

Abstract

In this article, we obtain an extension of the classical Hermite-Hadamard inequality for convex functions (concave functions) extending it to the power functions [f(x)]n{[f\left(x)]}^{n}. Some related inequalities are also introduced. By applying those results in analysis, we obtain new upper and lower bounds for the error function.

Keywords

• hermite-hadamard inequality
• jensen’s inequality
• convex function
• error function
• power function
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